A Zeroing Neurodynamic Approach for Solving Time-Varying Optimization Problem with Interval-Valued Cost Function

Most of the research on uncertainty and imprecision that is widespread in the real world can be abstracted into interval-valued optimization problems whose cost function or constraint function is a closed interval. In this paper, a zeroing neurodynamic (ZND) approach is designed for solving a class of constrained time-varying optimization problems with closed interval-valued cost functions. By virtue of the projection operator and the optimality conditions of the interval-valued optimization problem, the time-varying interval-valued optimization problem is transformed into a nonlinear equation system to be solved. For the reformulated nonlinear equation system, the proposed ZND solver has the ability to track its theoretical solution within pre-defined time. This significantly improves the convergence rate of the ZND solver, making the ZND solver more promising for complex engineering tasks. To the best of our knowledge, it is the first time applying the ZND solver to solve the time-varying interval value optimization problem. Furthermore, the introduction of the projection operator greatly reduces the computational complexity of this ZND solver, saving costs for its hardware implementation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.